This thesis presents an introduction to the three main fields that study time: physics, philosophy, and logics. A brief introduction to general relativity, thermodynamics and quantum physics is made. Also some of the basic ideas from the philosophy of time are explained and dualities connected to time are described, e.g. eternalism vs. presentism, determinism vs. indeterminism and the reality or unreality of time. As there is a huge number of temporal logics, only the main ideas that differentiate these logics from others are pointed out and some typical proofs are then shown. Special attention is then given to the relation between logics and physics, how the first can be used in the latter. Thereafter, Branching space-times and Branching continuation models are presented, which proved to be useful within quantum physics. Next, some basic terminology connected to general relativity and the A, P and T topologies are introduced . These are used together with the given models to investigate a possible combination.

This thesis is concerned with solitons (solutions of certain nonlinear partial differential equations) in certain cases when the underlying space is either a lattice or curved. Chapter 2 of the thesis is concerned with the outcome of collisions between a kink (a 1-dimensional soliton) and an antikink for certain topological discrete (TD) systems. The systems considered are the TD sine-Gordon and the TD ø(^4) For the TD sine-Gordon system it is found that the kink can support an internal shape mode which plays an important role during the collisions. In particular, this mode can be excited during collisions and this leads to spectacular resonance effects. The outcome of any particular collision has sensitive dependence on the initial conditions and could be either a trapped kink-antikink state, a "reflection" or a "transmission”. Such resonance effects are already known to exist for the conventional discrete ø(^4) system, and the TD ø(^4) system is no different, though the results for the two are not entirely similar. Chapter 3 considers the question of the existence of explicit travelling kink solutions for lattice systems. In particular, an expression for such a solution for the integrable lattice sine-Gordon system is derived. In Chapter 4, by reducing the Yang-Mills equations on the (2 + 2)-dimensional ultrahyperbolic space-time, an integrable Yang-Mills-Higgs system on (2 + 1) dimensional de Sitter space-time is derived. It represents the curved space-time version of the Bogomolny equations for monopoles on R(^3) . Using twister methods, various explicit solutions with gauge groups U(l) and SU(2) are constructed. A multi-solution SU(2) solution is also presented.

A thesis submitted in ful lment of the requirements for the degree of Master of Science in the Centre of Excellence in Telecommunications and Software School of Electrical and Information Engineering, March 2016 / In order to compare low rate error correcting codes to MIMO schemes with transmit diversity, two systems with the same throughput are compared. A VBLAST MIMO system with (15; 5) Reed-Solomon coding is compared to an Alamouti MIMO system with (15; 10) Reed-Solomon coding. The latter is found to perform signi cantly better, indicating that transmit diversity is a more e ective technique for minimising errors than reducing the code rate. The Guruswami-Sudan/Koetter-Vardy soft decision decoding algorithm was implemented to allow decoding beyond the conventional error correcting bound of RS codes and VBLAST was adapted to provide reliability information. Analysis is also performed to nd the optimal code rate when using various MIMO systems. / MT2016

[pt] O projeto de sistemas móveis em banda larga requer um planejamento detalhado devido à necessidade de maximizar a utilização da largura de banda disponível, maximizar a capacidade da rede, garantir requisitos mínimos de disponibilidade e minimizar os custos de implantação e operação da rede. Este trabalho apresenta uma metodologia de projeto a ser empregada em sistemas móveis em banda larga baseados no padrão IEEE 802.16e-2005 (WiMAX móvel). São apresentadas as novas tecnologias empregadas na elaboração do padrão, o modelo de propagação utilizado no cálculo de enlace, o cálculo da interferência co-canal, o cálculo da porcentagem de cobertura de área, o ganho de subcanalização e o cálculo da capacidade do canal. São analisadas abordagens para redução da interferência co-canal, visando maximizar a capacidade da rede e por fim é apresentado um estudo de caso utilizando uma ferramenta computadorizada de planejamento de redes móveis. / [en] The design of mobile broadband systems requires detailed planning due to necessity of maximizing the use of available bandwidth, network capacity, achieve minimum availability levels and minimize network implementation and operational costs. This work presents a design methodology to be employed in mobile broadband systems based on the IEEE Std 802.16-2005 (Mobile WiMAX). Here are presented the new technologies employed in the standard, the propagation model used for link budget, co-channel interference, coverage area percentage, sub-channelization gain and channel capacity calculations. Approaches for co-channel interference reduction are analyzed aiming to maximize network capacity and at the end a case study is presented using a computerized tool for mobile network planning.

O objetivo deste trabalho é comparar as estruturas de vizinhanças espaciais ou matrizes de pesos espaciais da classe de modelos autorregressivos e de médias móveis espaço-temporais (STARMA). O modelo STARMA é empregado para descrever dados de séries temporais espacialmente localizados, ele é caracterizado pela dependência linear defasada tanto no espaço quanto no tempo. Foram realizadas simulações utilizando vários modelos de covariância espaço-temporal para comparar diferentes estruturas de construção da matriz de pesos espaciais com a finalidade de identificar a melhor matriz. As matrizes espaciais com pesos exponenciais apresentaram os melhores desempenhos de ajuste dos modelos STAR; e mostram uma estabilidade em relação à medida de ajuste. Por fim para ilustração, será ajustado um modelo STARMA para um conjunto de dados mensais do índice FIPEZAP de preço imobiliário de venda para apartamentos de dois dormitórios de seis cidades metropolitanas de São Paulo. / The objective of this work is to compare spatial neighborhoods structures, or the same as spatial weights matrices of the class of space-time autoregressive and moving average models STARMA. The STARMA model is used to describe spatially localized time series datas, it is characterized by the linear dependence lagged both in space and time. Simulations were performed using several space-time covariance models to compare different structures of construction of the weight matrix with the purpose of identifying the best matrix. The spatial matrices with exponential weights presented the best adjustment performances of the STAR models ans showed a stability in relation to the adjustment measure. Finally, for illustration, a STARMA model will be adjusted for a set of monthly data of the FIPEZAP real estate price index for two bedroom apartments in six metropolitan cities of São Paulo.

O presente trabalho trata do problema da programação de entrega de concreto produzido em centrais dosadoras. Tal programação engloba as decisões de qual central deverá atender cada cliente e em qual horário cada veículo de entrega deverá ser carregado nessa central, de forma a maximizar a receita marginal total do sistema. São consideradas restrições de capacidade de carregamento de veículos por central, disponibilidade da frota, e garantia de atendimento de todos os pedidos de cada cliente por uma única central. A fim de resolver esse problema de forma eficiente, é proposto um modelo de programação matemática baseado em uma rede espaço-tempo, o qual foi implementado em ambiente de planilha eletrônica, como parte de um sistema de apoio à decisão. O sistema conta com uma interface amigável para o usuário, desenvolvida em linguagem VBA, que apresenta facilidade de preenchimento dos dados de entrada e compreensão dos resultados fornecidos, mesmo por aqueles sem conhecimento em pesquisa operacional. A aplicação do modelo proposto para a resolução de problemas com dados reais confirma que o modelo funciona corretamente, considera as restrições e gera rapidamente a solução ótima. Sendo assim, a ferramenta desenvolvida mostra-se bastante útil para as operações de programação de uma empresa concreteira que opera diversas centrais dosadoras de concreto. / This paper addresses the problem of scheduling concrete delivery produced in concrete batch plants. Such scheduling comprises the decisions of which center should serve each customer and what time each delivery vehicle should be loaded, so as to maximize the total marginal revenue of the system. Vehicle loading capacity constraints per center, fleet availability and the assurance that all orders will be fulfilled by a single concrete center are considered. In order to solve this problem efficiently, we propose a mathematical programming model based on a time-space network, implemented in a spreadsheet environment, as part of a decision support system. The system features a user-friendly interface, developed in VBA, which makes it easy to enter data and understand the results provided, even by those without knowledge in operational research. The implementation of the proposed model to solve problems with real data confirms that the model works properly, taking into consideration the constraints and quickly generating the optimal solution. Thus, the developed tool appears to be very useful for scheduling operations of a company which operates several concrete batch plants.

Introdução: O Estado de São Paulo, por compreender aproximadamente 40% dos casos de aids notificados no Brasil, oferece situação favorável para análise espaço-temporal, visando melhor compreensão da disseminação do HIV/aids. Objetivo: Avaliar a adequação de um modelo espaço-temporal para análise da dinâmica de disseminação da aids segundo áreas geográficas. Material e método: Foram utilizados os casos de aids notificados ao Sistema de Informação de Agravos de Notificação (SINAN - Ministério da Saúde) nos anos de 1990 a 2004 para pessoas com idade igual ou superior a 15 anos e foram criados os riscos relativos de ter aids segundo sexo para períodos de 3 anos utilizando modelos bayesianos completos supondo disseminação geográfica local e disseminação geográfica global. Resultados: O crescimento da aids no interior do Estado de São Paulo é apresentado claramente pelos modelos ajustados uma vez que entre os 50 municípios com maiores riscos relativos de aids no último período do estudo a maioria é do interior. As taxas estimadas de crescimento da aids para as mulheres foram, em sua maioria, de 200% a 300%, enquanto que para os homens este crescimento foi de 100% a 200%. Conclusão: O modelo bayesiano com disseminação global se mostrou mais adequado para explicação da epidemia de aids no Estado de São Paulo, pois não foi encontrada expansão espacial da aids no Estado, mas sim o crescimento local da doença. Os modelos corroboram os fenômenos de feminização e interiorização descritos à exaustão na literatura, o que indica suas adequações. / Introduction: The State of São Paulo, with approximately 40% of the notified cases of AIDS in Brazil, offers a favorable opportunity for a space-time analysis of this disease, which can provide a better understanding of the dissemination of the HIV/AIDS. Objective: To evaluate the adequacy of on space-time modeling to analyze the dynamics of AIDS dissemination according to geographic areas. Methods: Cases of AIDS reported to the Sistema de Informação de Agravos de Notificação (National Disease Reporting System) (SINAN - Ministry of Health) from 1990 to 2004, for people aged 15 years or older were selected. Relative risks of aids for each sex for periods of 3 years were created using complete bayesians models assuming local and global geographic dissemination. Results: The performed analyzes showed that these models were adequate to explain the AIDS dissemination in the State of São Paulo and clearly showed the processes of growth among females and in small size cities. Among the 50 cities with the largest relative risks of AIDS in the last period of study the majority were in the countryside. In general estimated growth rates of AIDS among females were between 200% and 300% while for males were between 100% and 200%. Conclusion: The bayesian model with global dissemination was more adequate to explain the AIDS epidemic in the State of São Paulo since no spatial spreading was observed but instead a local expansion of the disease. The models were consistent with the processes of growth among females and in small size cities, described in the literature indicating their adequacy.

O objetivo deste trabalho é comparar as estruturas de vizinhanças espaciais ou matrizes de pesos espaciais da classe de modelos autorregressivos e de médias móveis espaço-temporais (STARMA). O modelo STARMA é empregado para descrever dados de séries temporais espacialmente localizados, ele é caracterizado pela dependência linear defasada tanto no espaço quanto no tempo. Foram realizadas simulações utilizando vários modelos de covariância espaço-temporal para comparar diferentes estruturas de construção da matriz de pesos espaciais com a finalidade de identificar a melhor matriz. As matrizes espaciais com pesos exponenciais apresentaram os melhores desempenhos de ajuste dos modelos STAR; e mostram uma estabilidade em relação à medida de ajuste. Por fim para ilustração, será ajustado um modelo STARMA para um conjunto de dados mensais do índice FIPEZAP de preço imobiliário de venda para apartamentos de dois dormitórios de seis cidades metropolitanas de São Paulo. / The objective of this work is to compare spatial neighborhoods structures, or the same as spatial weights matrices of the class of space-time autoregressive and moving average models STARMA. The STARMA model is used to describe spatially localized time series datas, it is characterized by the linear dependence lagged both in space and time. Simulations were performed using several space-time covariance models to compare different structures of construction of the weight matrix with the purpose of identifying the best matrix. The spatial matrices with exponential weights presented the best adjustment performances of the STAR models ans showed a stability in relation to the adjustment measure. Finally, for illustration, a STARMA model will be adjusted for a set of monthly data of the FIPEZAP real estate price index for two bedroom apartments in six metropolitan cities of São Paulo.

This work deals with the design of a hybrid time integrator that couples spatially explicit and implicit time integrators. In order to cope with the industrial solver of Ariane Group called FLUSEPA, the explicit scheme of Heun and the implicit scheme of Crank-Nicolson are hybridized using the transition parameter : the whole technique is called AION time integration. The latter is studied into details with special focus on spectral behaviour and on its ability to keep the accuracy. It is shown that the hybrid technique has interesting dissipation and dispersion properties while maintaining precision and avoiding spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. And as expected the method is more interesting in term of computational time than standard time integrators. For the extension of this hybrid approach to the temporal adaptive method implemented in FLUSEPA, it was necessary to improve some treatments in order to maintain conservation and acceptable spectral properties. Finally the hybrid time integration was also applied to a RANS/LES turbulent test case with interesting computational time while capturing the flow physics.

The exploitation of the theoretically enormous capacity achieved by the multiple transmit and receive antennas systems (MIMO) in a rich scattering communication channel has been the subject of vast body of research on the field of MIMO. In particular, the Vertically-layered Bell Laboratories Layered Space-Time (V-BLAST) is a well known MIMO architecture which has demonstrated the enormous capacity of 20-40 bit/s/Hz in an indoor propagation environment with realistic SNR and error rates. However, due to the intensive computation involved, it would be difficult to implement this architecture for high data rate communication systems. Some works have been done to improve the receiver complexity and performance by coding techniques, by different detection architectures. In this thesis, we have focused on QR-based decoders for V-BLAST MIMO. For a suitable V-BLAST detection implementation, we need to carefully consider the problem from algorithmic, arithmetic and architectural aspects. At the algorithmic level, the numerical stability and robustness should be considered. At the arithmetic level, signal quantization is important, and, at the architectural level, parallelism and pipelining require attention. We have performed the above mentioned optimization on the 1-pass QR factorization with back substitution SIC (Symbol Interference Cancellation) decoder in chapter 3. At first optimizations are made on the proposed algorithm and architecture using MATLAB simulations. Then a new architecture for the QR-factorizer as the core processor of the V-BLAST decoder is developed in chapter 4. This architecture uses only two low complexity CORDIC (Coordinate rotation digital computer) processors. The parameterized feature of the controller and address generator blocks of this architecture has provided a scalable architecture for the implementation of QR factorization for square matrix of any dimension. The reduced hardware complexity of the processors and its simple parameterized controller are two outstanding features of the architecture, resulting in a more suitable alternative architecture for QR factorization than traditional triangular systolic arrays. In the next phase of the research, new hardware architectures of the back substitution SIC decoder was developed for a 4 X 4 MIMO system with 16-QAM constellation scheme in chapter 5. The division operation for back substitution needs a complex hardware, and results in the numerical instability. In the proposed hardware the elimination of division and modification of multiplier has reduced the hardware complexity and led to numerical stability. In addition the pre decoding block was designed and optimized in terms of number of the pipeline registers and CORDIC rotator processors. The developed hardware is capable of processing 20 vectors data burst and results in a throughput of 149 Mb/s. The FPGA (Field Programmable Gate Array) and ASIC (Application specific Integrated Circuit) implementations of the proposed optimized architecture are presented in Chapter 5. We found that the equivalent gates and the core area in our design is less than 30% of other designs and the maximum clock frequency and the throughput is higher (175 %) than other works. Finally the improvements of the BER performance using the branching method and parallel architectures are presented in chapter 6. In this supplementary part to back substitution OSIC decoder, the final symbol vector is selected from 2 or 8 potential candidates based on the minimum Euclidean norm, which improves the BER between 3 to 7 db and gives a very close match to the original V-BLAST performance.